Question 211: Waves Optics

Question

In Young's double slit experiment, two slits $$S_{1}$$ and $$S_{2}$$ are '$$d$$' distance apart and the separation from slits to screen is $$\mathrm{D}$$ (as shown in figure). Now if two transparent slabs of equal thickness $$0.1 \mathrm{~mm}$$ but refractive index $$1.51$$ and $$1.55$$ are introduced in the path of beam $$(\lambda=4000$$ $$\mathop A\limits^o $$) from $$\mathrm{S}_{1}$$ and $$\mathrm{S}_{2}$$ respectively. The central bright fringe spot will shift by ___________ number of fringes.

Accepted Answer

Path difference introduced by two slabs $$=(\mu_2-\mu_1)t$$
$$\Rightarrow$$ Number of shifts $$ = {{({\mu _2} - {\mu _1})t} \over \lambda }$$
$$ = {{0.04 	imes 0.1\,\mathrm{mm}} \over {4000\,\mathop A\limits^o }}$$
$$ = {{4 	imes {{10}^{ - 2}} 	imes {{10}^{ - 4}}} \over {4 	imes {{10}^{ - 7}}}} = 10$$

Waves Optics

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